Suppose you have a bag with 6 blue marbles and 4 red marbles. Calculatethe following probabilities:a) If you randomly remove half of the marbles from the bag, what is the probability that 3 of them are blue and 2 are red?b) Suppose that you sample with replacement from the bag: you take out a marble, record its color, then throw it back in. What is the probability that you need to repeat this process exactly 10 times before seeing your first red marble on your 10th selection?c) Again sampling with replacement, what is the probability that you need to repeat the process exactly 10 times before seeing your 4th red marble on your 10th selection?d) Again sampling with replacement, what is the probability that if you sample 10 times, exactly 4 of your marbles are red?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose you have a bag with 6 blue marbles and 4 red marbles. Calculate
the following probabilities:
a) If you randomly remove half of the marbles from the bag, what is the
b) Suppose that you sample with replacement from the bag: you take out a marble, record its color, then throw it back in. What is the probability that you need to repeat this process exactly 10 times before seeing your first red marble on your 10th selection?
c) Again sampling with replacement, what is the probability that you need to repeat the process exactly 10 times before seeing your 4th red marble on your 10th selection?
d) Again sampling with replacement, what is the probability that if you sample 10 times, exactly 4 of your marbles are red?
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